yes, they can be a bit tricky at first
think about small numbers
first the definition as I like to give it:\[\huge\log_ax=b\text{ if }a^b=x\]in other words\[\large \log_ax\]asks
"what power do we raise a to in order to get x?"
for example...

I'm glad, it helps me!
and in general\[\log_aa=1\]now look at\[\log_2(16)\]if we factor 16 we get\[\log_2(2^4)\]now apply the third rule\[4\log_2(2)=4(1)=4\]so we get the answer we already knew
it also shows that\[\log_aa^x=x\]which is nice to know that's how I did your earlier problem)
so by factoring and using these rules we can break down lots of numbers with logs